554 



THE LOGAKITHMIC SPIRAL 



[CH. 



in the generating curve is, in all cases, a logarithmic spiral. In 

 discoid shells, the generating figure revolves in a plane perpendicular 

 to the axis, as in Nautilus, the Argonaut and the Ammonite. 

 In turbinate shells, it slides continually along the axis of revolu- 

 tion, and the curve in space generated by any given point partakes, 

 therefore, of the character of a helix, as well as of a logarithmic 

 spiral ; it may be strictly entitled a helico-spiral. Such turbinate 

 or helico-spiral shells include the snail, the periwinkle and all the 

 common typical Gastropods. 



The generating figure, as represented by the mouth of the 

 shell, is sometimes a plane curve, of simple form; in other and 

 more numerous cases, it becomes more complicated in form and 

 its boundaries do not lie in one plane : but in such cases as these 

 we may replace it by its "trace/' on a 

 plane at some definite angle to the direction 

 of growth, for instance by its form as it 

 appears in a section through the axis of 

 the hehcoid shell. The generating curve 

 is of very various shapes. It is circular 

 in Scalaria or Cyclostoma, and in Spirula; 

 it may be considered as a segment of a 

 circle in Natica or in Planorbis. It is 

 approximately triangular in Conus, and 

 rhomboidal in Solarium or Potamides. It 

 is very commonly more or less elliptical : 

 the long axis of the ellipse being parallel 

 to the axis of the shell in Oliva and Cypraea ; 

 all but perpendicular to it in many Trochi ; 

 and obhque to it in many w-ell-marked 

 cases, such as Stomatella, Lamellaria, 

 Sigaretus haliotoides (Fig. 284) and HaUotis. 

 In Nautilus pompilius it is approximately 

 a semi-ellipse, and in N. umbilicatus rather 

 more than a semi-ellipse, the long axis 

 Jying in both cases perpendicular to the axis of the shell*. Its 



Fig. 283. Section of a spiral, 

 or turbinate, univalve, 

 Triton corrugatus. Lam. 

 (From Woodward.) 



* In Nautilus, the "hood" has somewhat different dimensions in the two 

 sexes, and these differences are impressed upon the shell, that is to say upon its 

 "generating curve." The latter constitutes a somewhat broader ellipse in the 



